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arXiv:1912.04919 · Physical review. B./Physical review. B

Wiedemann-Franz law in a non-Fermi liquid and Majorana central charge: Thermoelectric transport in a two-channel Kondo system

G.A.R. van Dalum, Andrew K. Mitchell, Lars Fritz

Published Jul 8, 2020• 30 citations
arXivHTMLPDF

Abstract

Quantum dot devices allow one to access the critical point of the two-channel Kondo model. The effective critical theory involves a free Majorana fermion quasiparticle localized on the dot. As a consequence, this critical point shows both the phenomenon of non-Fermi-liquid physics and fractionalization. Although a violation of the Wiedemann-Franz law is often considered to be a sign of non-Fermi-liquid systems, we show by exact calculations that it holds at the critical point, thereby providing a counterexample to this lore. Furthermore, we show that the fractionalized Majorana character of the critical point can be unambiguously detected from the heat conductance, opening the door to a direct experimental measurement of the elusive Majorana central charge $c=\frac{1}{2}$.

DOI
10.1103/physrevb.102.041111

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Quantum dot devices allow one to access the critical point of the two-channel Kondo model. The effective critical theory involves a free Majorana fermion quasiparticle localized on the dot. As a consequence, this critical point shows both the phenomenon of non-Fermi-liquid physics and fractionalization. Although a violation of the Wiedemann-Franz law is often considered to be a sign of non-Fermi-liquid systems, we show by exact calculations that it holds at the critical point, thereby providing a counterexample to this lore. Furthermore, we show that the fractionalized Majorana character of the critical point can be unambiguously detected from the heat conductance, opening the door to a direct experimental measurement of the elusive Majorana central charge c=12c=\frac{1}{2}c=21​.
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Motivated by the experimental realization of a multi-channel charge Kondo device [Iftikhar et al., Nature (London) 526, 233 (2015)], we study generic charge and heat transport properties of the charge two-channel Kondo model. We present a comprehensive discussion of the out-of-equilibrium and time-dependent charge transport, as well as thermal transport within linear response theory. The transport properties are calculated at, and also in the vicinity of, the exactly solvable Emery-Kivelson point, which has the form of a Majorana fermion resonant level model. We focus on regimes where our solution gives exact results for the physical quantum dot device, and highlight new predictions relevant to future experiments.
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Unconventional quantum states defying the ubiquitous Fermi-liquid paradigm can emerge in the presence of strong electronic correlations. Among these, non-Abelian anyons - such as Majorana zero modes and Fibonacci anyons - are of particular interest for topological quantum computing due to their non-integer quantum dimensions d>1, which allows for protected non-local encoding and processing of quantum information. However, despite considerable efforts, the unambiguous characterisation of such anyons via transport measurements has proved challenging. Instead, here we provide experimental evidence for the low-temperature fractional entropy Delta S associated with a single anyon, which directly implies its non-Abelian character through the relation Delta S = kB ln(d). This thermodynamic signature is measured in metal-semiconductor quantum circuits engineered to realize quantum-critical states from frustrated interactions. Using a micrometre-scale metallic island coupled to two or three electronic leads, we tune the system to two-channel and three-channel Kondo critical points. By measuring the island charge and exploiting a thermodynamic Maxwell relation, we estimate the entropy associated with the anyons that emerge in these critical states. Our observations reveal fractional values, exposing non-Abelian anyons. The corresponding scaling dimensions are consistent with theoretical predictions for a Majorana zero mode Delta S = kB ln(sqrt(2)) and a Fibonacci anyon Delta S = kB ln(1 +sqrt(5))/2 for two and three channels. These findings establish entropy measurements as a powerful tool for characterizing exotic quantum states.
Department of Physics, Harvard University, Cambridge, MA 02138(Dated: Printed February 2, 2008)We study electric, thermal, and thermoelectric conductivities in the vicinity of a z = 2superconductor-diffusive metal transition in two dimensions, both in the high and low frequencylimits. We find violation of the Wiedemann-Franz law and a dc thermoelectric conductivity α thatdoes not vanish at low temperatures, in contrast to Fermi liquids. We introduce a Langevin equationformalism to study critical dynamics over a broad region surrounding the quantum critical point.INTRODUCTION
Over recent decades, a growing number of systems, many of them quantum critical, have been shown to exhibit non-Fermi-liquid behavior, but a full analytic understanding of such systems out of equilibrium is still lacking. In this paper, we provide a distinct example with broad applications in correlated mesoscopic systems to address this issue---a two-channel Kondo-Luttinger model where a Kondo impurity couples to two voltage-biased interacting electron leads, experimentally realizable in a dissipative quantum dot. Therein, an exotic quantum phase transition has been known to exist since the 1990s from the one-channel to two-channel Kondo ground states by enhancing electron interactions in the leads, but a controlled analytic approach to this quantum critical point has not yet been established due to the breakdown of weak-coupling perturbation theory near this strong-coupling critical point. We present a controlled method to this long-standing problem by mapping the system in the strong-coupling regime to an effective spin-boson-fermion Hamiltonian. Another type of non-Fermi-liquid quantum critical point is discovered with a distinct logarithmic-in-temperature and -voltage dependence in transport. We further obtain an analytical form for the universal differential conductance out of equilibrium near the transition. Our approach can be further generalized to study nonequilibrium physics of other strong-coupling low-dimensional non-Fermi-liquid fixed points. The relevance of our results for recent experiments is discussed.